A numerical simulation study of gallium-phosphide/silicon heterojunction passivated emitter and rear solar cells

A numerical simulation study of gallium-phosphide/silicon heterojunction passivated emitter and rear solar cells
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  A numerical simulation studyof gallium-phosphide/silicon heterojunctionpassivated emitter and rearsolarcells Hannes Wagner, 1,2 Tobias Ohrdes, 3 Amir Dastgheib-Shirazi, 4 Binesh Puthen-Veettil, 2 Dirk K € onig, 2 and Pietro P. Altermatt 1 1  Department of Solar Energy, Institute Solid-State Physics, Leibniz University of Hannover, Appelstr. 2, 30167 Hannover, Germany 2  ARC Photovoltaics Centre of Excellence, University of New South Wales (UNSW), Sydney, NSW 2052, Australia 3  Institute for Solar Energy Research Hamelin (ISFH), 31860 Emmerthal, Germany 4  Div. Photovoltaics, Department of Physics, University of Konstanz, 78457 Konstanz, Germany (Received 24 October 2013; accepted 15 January 2014; published online 28 January 2014)The performance of passivated emitter and rear (PERC) solar cells made of p-type Si wafers isoften limited by recombination in the phosphorus-doped emitter. To overcome this limitation, arealistic PERC solar cell is simulated, whereby the conventional phosphorus-doped emitter isreplaced by a thin, crystalline gallium phosphide (GaP) layer. The resulting GaP/Si PERC cell iscompared to Si PERC cells, which have (i) a standard POCl 3  diffused emitter, (ii) a solid-statediffused emitter, or (iii) a high efficiency ion-implanted emitter. The maximum efficiencies for these realistic PERC cells are between 20.5% and 21.2% for the phosphorus-doped emitters(i)–(iii), and up to 21.6% for the GaP emitter. The major advantage of this GaP hetero-emitter is asignificantly reduced recombination loss, resulting in a higher   V  oc . This is so because the highvalence band offset between GaP and Si acts as a nearly ideal minority carrier blocker. This effectis comparable to amorphous Si. However, the GaP layer can be contacted with metal fingers likecrystalline Si, so no conductive oxide is necessary. Compared to the conventional PERC structure,the GaP/Si PERC cell requires a lower Si base doping density, which reduces the impact of theboron-oxygen complexes. Despite the lower base doping, fewer rear local contacts are necessary.This is so because the GaP emitter shows reduced recombination, leading to a higher minorityelectron density in the base and, in turn, to a higher base conductivity. V C  2014 AIP Publishing LLC .[] I. INTRODUCTION The passivated emitter and rear (PERC) solar cells 1 presently being developed for industrial mass productionare often limited by the recombination losses in theemitter, because the emitter is usually produced byPOCl 3 -diffusion. The major disadvantages of this diffusionprocess, generally, are: (i) the high surface concentration  N  surf  , above 10 20 cm  3 , causing a high surface recombina-tion velocity  S  front  , (ii) the large amount of Auger recombi-nation due to the high dopant concentration, and (iii) largeShockley-Read-Hall (SRH) recombination losses due toelectrical non-active phosphorus. 2 This non-active phos-phorus occurs when phosphorus concentrations exceed thesolubility limit in Si.One way to reduce  N  surf   and the amount of Auger andSRH recombination is to use solid-state diffusion or ion-implant technologies. These techniques reduce  N  surf   and,consequently,  S  front  .  In addition, the solubility limit of P isusually not reached, causing only an insignificant amount of non-electrical active phosphorus. At the same time, Auger recombination is reduced due to there being fewer electricalactive dopants.Another promising way to reduce recombination is toreplace the conventional emitter with other semiconductor materials. A significant increase in performance has beendemonstrated by using amorphous Si (a-Si) layers. 3 In this work, we investigate the potential improvementsdue to an emitter made of gallium phosphide (GaP). Wechoose GaP because of its promising characteristics. First,the lattice mismatch to Si is smaller than 0.4%, so the growth of a crystalline layer is feasible, 4 – 8 and there is low recombi-nation at the interface to Si. Second, the free carrier mobilityis comparable to crystalline Si and is much higher than themobility in amorphous Si. Third, the bandgap  E G  of galliumphosphide is larger (2.26eV) than that of Si (1.12eV). Thiscreates the potential to use it as a minority carrier blocker,like in other heterostructures. Fourth, experimental proof for a GaP/Si solar cell was first reported in 1988 and was pro-duced by heteroepitaxy. 9 Here, numerical device simulations are performed toestimate which conversion efficiency  g  of GaP/Si PERCcells can be reasonably expected in mass production. II. METHODSA. Simulation model Figure 1 shows a schematic illustration of a PERC solar cell as simulated here. Four different types of emitters areused during the simulations:1. A conventional phosphorus emitter, formed by a phosphosi-licate glass layer (PSG) usually deposited by POCl 3 , as iscommonly done in industrial mass production. Its 0021-8979/2014/115(4)/044508/6/$30.00  V C  2014 AIP Publishing LLC 115 , 044508-1 JOURNAL OF APPLIED PHYSICS  115 , 044508 (2014)   N  surf  ¼ 2.92  10 20 cm  3 causes a  S  front  ¼ 1.3  10 5 cm/s, 10 its junction depth  d   junct  is 0.54 l m, and its sheet resistivity q sheet  is 67.4 X  /sq.2. An emitter produced by solid-state diff usion, having  N  surf  ¼ 2.15  10 19 cm  3 ,  S  front  ¼ 8000cm/s, 10 d   junct ¼ 0.93 l m,and  q sheet ¼ 93.4 X  /sq.3. An ion-implanted emitter with  N  surf  ¼ 5  10 18 cm  3 , S  front  ¼ 337cm/s, 11 d   junct ¼ 1.08 l m, and  q sheet ¼ 276.5 X  /sq. This eliminates any significant surface recombina-tion and greatly reduces Auger recombination.4. A thin, crystalline n-type GaP layer is formed on top of the Si wafer. Its uniform dopant density is kept free, andits  S  front   value is set to 1000cm/s. It is shown later that S  front   has almost no influence on cells efficiency.Since we mainly vary the emitter, we use the followingabbreviations: The PERC cell with the PSG emitter is called  PSG cell , the cell with the solid-state diffused emitter   solid-state cell , the cell with the ion-implanted emitter   ion cell, and the cell with a the gallium-phosphide emitter   GaP cell .All cells have the same local Al-BSF 12 covering the rear finger-shaped contacts to a width of 100 l m. The front andrear surfaces are passivated with dielectrics. We assume S rear  ¼ 10cm/s, a value which has been experimentally real-ized with Al 2 O 3 , e.g., in Ref. 13. In the boron-doped Si wa-fer, we account for boron-oxygen complexes and use themodel for recovered SRH lifetimes proposed by Schmidt et al. 14 The remaining model parameters for silicon are takenfrom Ref. 15.The model parameters for gallium phosphide are takenfrom various literature sources. The coefficient for radiativerecombination is  C  Rad  ¼ 1  10  13 cm 3  / s, 16 for Auger recombination  C  Auger  ¼ 2.81  10  31 cm 6  /s, 17 and from Ref.18, it is estimated that the lowest SRH recombination life-time is no smaller than 0.1 l s. The minimum (indirect)bandgap of GaP is set to 2.261eV at 300K from Ref. 19.The electron affinity  v ¼ 3.8eV is chosen from Ref. 20. Theeffective density of states  N  c ¼ 1.9  10 19 cm  3 is obtainedfrom the density of states mass  m e ¼ 0.83 from Ref. 21, and  N  v ¼ 1.4  10 19 cm  3 from  m h ¼ 0.68 from Ref. 22. Adoping-dependent bandgap narrowing model is implementedas described in Ref. 23. The doping-dependent carrier mobi-lities are taken from Ref. 24, while for doping concentrations > 10 19 cm  3 , the mobility is scaled to Ref. 25, meaning thatthe shape of the curve is assumed to be identical betweencrystalline silicon and crystalline GaP. We includephonon-assisted direct tunneling through the steep p-n junction from the Si valence band to the GaP conductionband, using Schenk’s tunneling model. 26 All simulations are carried out at 1-sun and 300K, usingthe software Sentaurus Device (also called Dessis or TCAD 27 ). The optical generation within the planar, untex-tured wafers is modeled by ray tracing using the softwareSunrays. 28 We use planar surfaces to avoid any uncertaintiesthat might come from a texture. The resulting IV-curves arecorrected by metal shading and resistive losses in the metalli-zation, as typically experienced in 15.6  15.6 cm 2 solar cells. B. Optimiziation model To achieve the maximum efficiency for each type of emitter in the PERC cells, we vary the following parametersin a simulation study: the homogeneous boron doping con-centration  Si dop  in silicon, the spacing between the local rear contacts  d  rear  , and the spacing between the front contacts d   front  . Additionally, for GaP, the homogeneous doping con-centration in gallium phosphide,  GaP dop , and the GaP layer thickness,  d  GaP , are varied.These input parameters influence cell efficiency in amutually dependent manner. For example, the band-bendingin the p-n junction between GaP and Si depends on the dop-ing concentrations in both  Si dop  and  GaP dop . A commonapproach to finding the optimum combination of the inputparameters would be to simulate all possible combinationsbetween the different input parameters. From the simulatedIV curves, the characteristic output parameters  J  sc ,  V  oc ,  FF ,and  g  are compared in order to find the optimum combina-tion between the input parameters. This approach has themajor disadvantage of needing a very large number of simulations.To avoid this, we choose an approach where we com-bine our numerical device simulations with a design of experiment (DOE) approach. In the DOE, all input parame-ters for the device model are varied concurrently using a sta-tistical method. This greatly reduces the number of combinations of input parameters compared to the approachdescribed above. The simulated output parameters  J  sc ,  V  oc ,  FF , and  g  are then fitted with polynomial expressions in aregression analysis, using the so-called Response SurfaceMethodology (RSM). While this approximates the correla-tion between input and output parameters, it is important tonote that it contains all the mutual interactions among theinput parameters, even though a greatly reduced number of simulations were carried out. Only the polynomials are usedto maximize  g ; no additional device simulations are per-formed. Because the polynomials are approximate, we per-form some test device simulations, and we may need torepeat the DOE with a restricted range of input parameters.Even if the DOE needs to be iterated, the number of devicesimulations is still gr eatly reduced. The DOE and RSM arecalculated using JMP. 29 C. Recombination loss analysis For a loss analysis, the PERC solar cell is divided intothree different regions. The front side contains the emitter, FIG. 1. Illustration of a PERC solar cell as simulated here. Different emit-ters, listed in Table I, are compared. The local back contacts and the localAl-BSFs are included at the Al 2 O 3 -passivated rear side of the structure. 044508-2 Wagner  et al.  J. Appl. Phys.  115 , 044508 (2014)  the front passivation, and front contacts. The base regioncontains the wafer between the emitter and the BSF. Therear side contains the BSF, the rear-side passivation, andlocal rear contacts. All recombination rates caused by radia-tive, Auger, and SRH, at the interfaces, as well as band-to-band tunneling, are integrated within these separate deviceregions and multiplied by the unit charge to arrive at units of current density. In this way, the recombination losses at thefront, base and rear side in a cell can be compared. III. RESULTS AND DISCUSSIONA. Optimumcell parametersfordifferent emitters Table I shows the resulting maximum IV-curve parame-ters of the four types of optimized PERC solar cells. TheGaP cell has the highest efficiency value of 21.6%, followedby the ion cell with 21.2%, the solid-state cell with 21.0%,and the PSG cell with 20.5%.The difference in  J  sc  is minor, as is the difference in  FF .The major difference between the cells is caused by  V  oc ,which varies up to 49mV because it is most sensitive to therecombination rate: a higher   V  oc  value indicates a lower recombination rate in the cell. Because all cells have nearlythe same base doping in Si, equal geometry, and identicallocal rear BSFs, most of the differences in recombinationoccur in the emitter region. A detailed analysis of this behav-ior is presented in Sec. IIIB.The resulting optimum base doping in Si decreases from2.61  10 15 cm  3 in the case of the PSG cell, to 6.23  10 14 cm  3 for the GaP cell, as also listed in Table I. A reductionin base doping causes a reduction in boron-oxygen com-plexes within the wafer material and hence a better SRHbulk lifetime. 13 The optimum doping concentration in theGaP layer would be 1.94  10 20 cm  3 , but a concentration aslow as 3  10 19 cm  3 still leads to a clear efficiency advant-age compared to the Si PERC cells, as is analyzed in moredetail in Sec. IIIC.The optimum metal finger distances at the front and therear sides also vary between the different types of emitters.The cells with a phosphorus emitter need 5 local rear con-tacts between 2 front contacts for maximum efficiency,whereas the GaP cell needs only 3 rear contacts between 2front contacts, with the optimum distance between two frontcontacts given in Table I. This is so because the GaP emitter shows reduced recombination, leading to a higher minorityelectron density in the base and, in turn, to a higher baseconductivity. B. Emitter loss analysis In order to understand the large difference in  V  oc between the four different emitters, a more detailed look atthe recombination is helpful. Figure 2 shows the recombina-tion current densities in the emitter, the base, and the rear region, depending on bias, for the four cells, as explained inSec. IIC. The cells with phosphorus emitters show a clear tendency: the recombination current decreases with decreas-ing phosphorus dopant concentration. This decrease is due todecreasing Auger recombination, which depends quadrati-cally on the dopant concentration. In addition,  S  front  decreases from the standard emitter to the ion-implantedemitter. In the PSG cell, the effect of higher SRH recombina-tion due to electrical non-active phosphorus 2 is not takeninto account in this study.In an open-circuit condition, the emitter recombinationlosses dominate in the PSG cell, while in the solid-state cell,the losses at the rear side become more significant and evendominant in the ion cell. A totally different behavior is seenin the case of a GaP emitter. With increasing bias, only asmall increase in the recombination current density in theemitter region is observed, meaning that, under open-circuitconditions, recombination in the base and at the rear sidedominates. This small increase in emitter loss current densityin the GaP cell, relative to the other cells, explains the signif-icant increase in  V  oc  and  g  in the GaP cell.To understand the small increase in the recombinationcurrent in the GaP emitter at high bias, a more detailed anal-ysis of the band structure is helpful. In the case of the phos-phorus emitters, a forward voltage reduces the band bendingin the valence band across the p-n junction. As a result, thedensity of minority carriers (holes) in the emitter regionincreases, as does recombination. Figure 3 shows the minor-ity carrier densities in the emitter regions for the four cells.This increases strongly toward  V  oc  for the phosphorus emit-ters. For the GaP emitter, it is nearly constant, remaining atvery low concentrations, meaning that insufficient minoritycarriers are available for recombination with electrons.Consequently, a very small increase in loss is observable for the GaP emitter (see Fig. 2).Finally, the low minority carrier concentration in GaPcan be explained with the band diagram of the GaP/Si cellunder   V  oc  conditions (cf. Figure 4). GaP has a very highvalence-band offset to Si, which makes it an excellent hole-blocking layer. This significantly reduces both the intrinsiccarrier density and the number of holes, compared to a con-ventional phosphorus-doped Si emitter. The recombinationrate increases slightly at large bias in Fig. 2 due to band-to-band tunneling at the interface between GaP and Si. Theinfluence of the interface and the surface recombination isdiscussed in Sec. IIIC. TABLE I. List of parameters for the three chosen phosphorus emitters, for the optimized GaP emitter, for the IV-curve parameters yielding maximizedcell efficiencies, and for their corresponding optimum device parameters.Emitter PSG cell Solid-state cell Ion cell GaP cell  N  surf   (cm  3 ) 2.92  10 20 2.15  10 19 5.0  10 18 1.94  10 20 S front  (cm/s) 1  10 5 8000 337 1000 q sheet  67 93 276 462 d   junct  ( l m) 0.54 0.93 1.08 0.01V oc  (mV) 661 677 683 710J sc  (mA/cm 2 ) 37.98 38.20 38.53 37.68FF (%) 81.57 81.12 80.61 80.70 g  (%) 20.5 21.0 21.2 21.6 Si dop  (cm  3 ) 2.61  10 15 1.72  10 15 1.00  10 15 6.23  10 14 GaP dop  (cm  3 ) … … … 1.94  10 20 d   front   ( l m) 1400 1610 1650 1400 d  rear   ( l m) 350 402.5 412.5 700  # rear contacts  5 5 5 3 044508-3 Wagner  et al.  J. Appl. Phys.  115 , 044508 (2014)  C. Further investigations of GaP/Si solar cell In cell design, the doping densities are one of the mostimportant parameters. The predicted optimum values for  Si dop  and  GaP dop  were discussed in Sec. IIIA and given inTable I. We now investigate how deviations from these opti-mum values reduce cell efficiency.Fig. 5 shows the GaP/Si PERC cell efficiency when de-pendent on  Si dop  and  GaP dop  while keeping all other parame-ters at their optimum values, as described in Sec. IIIA. Cell’sefficiency decreases with higher   Si do p  due to the decreasingSRH lifetime in the base material. 14 An excessively low GaP dop  significantly increases the sheet resistivity, leading todecreased FF and  g  due to lateral current transport in the GaPemitter. Both  V  oc  and  J  sc  remain rather unaffected, indicatingthat the recombination losses in the GaP emitter do not domi-nate device behavior. An excessively high  GaP dop  alsoreduces efficiency, due to low carrier mobility and high Auger recombination losses, while band-gap narrowing leads to anincrease in band-to-band tunneling.In general, it can be stated that over a wide range of  Si dop  and  GaP dop  the efficiency of the GaP/Si PERC cell israther unaffected, in contrast to well-known strong dopingdependences in homojunction PERC solar cells. The main FIG. 2. Simulated recombination current densities for PERC solar cells with a PSG diffused emitter, a solid-state diffused emitter, an ion implanted emitter,and an n-doped gallium phosphide emitter. The losses are divided into three different regions: the emitter, the base region, and the rear side.FIG. 3. Simulated average minority carrier densities (holes) in the emitter region for PERC solar cells with a PSG diffused emitter, a solid-state dif-fused emitter, an ion implanted emitter, and an n-type GaP emitter. The mi-nority carrier density in the phosphorus emitters strongly increases towards V  oc ; however, it stays nearly constant in the GaP emitter due to the valenceband offset depicted in Fig. 4. 044508-4 Wagner  et al.  J. Appl. Phys.  115 , 044508 (2014)  reason for this is the electric field at the interface betweenemitter and base, which blocks the number of minority car-rier densities moving from base material in the emitter region. In case of homojunction PERC cells, the field is notsufficient high for higher applied voltages and a strongincrease of minority carriers (Fig. 3) gives large recombina-tion losses (Fig 2). In case of a GaP/Si heterojunction PERCcell, the high valence band offset (Fig. 4) is rather unaffectedby changes in applied voltages. Consequently, minority car-riers are blocked and only little increase in recombinationcurrent in the GaP emitter is observed (Fig. 2).The electron affinity of GaP,  v , influences the band dia-gram rather strongly. In Fig. 6, we vary  v  from its defaultvalue  v ¼ 3.8eV from Ref. 20, while keeping the dopingdensities constant (possibly leading to non-optimized effi-ciency values). Additionally, the surface recombination ve-locity in the hetero-interface S het  is varied.Overall, the cell efficiency is rather insensitive to  v . Atlower values for   v , a small drop in efficiency is caused by anincreasing spike (visible in Fig. 4 at 10 nm depth), whichreduces the current lightly. At very high  v , a strong decreasein efficiency is caused by a significant increase of majoritycarriers (holes) at the Si side of the interface. This leads to adramatic increase in the interface recombination rate. Figure6 shows that  S het  strongly influences cell efficiency only at v > 4eV, making GaP/Si heterostructures a candidate where S het  plays an unimportant role.Finally, we simulate the GaP/Si PERC cell efficiencywhen dependent on the surface and hetero-interface recombi-nation velocities S front , S rear  , and S het , while keeping all other parameters at their optimum values, as given in Table I.Figure 7 shows that the efficiency decreases sensitively withincreasing S rear  . This effect is well-known in PERC celldesign and caused mainly by two effects: first, a high S rear  causes many minority carriers in the base to diffuse to therear instead of to the front p-n junction, and second, thequasi-Fermi level separation in the base becomes rather strongly coupled to the rear and hence is reduced. In contrast,only minor efficiency losses are predicted for increasing val-ues of S front  and S het . The main reason for this is the low mi-nority carrier density in the emitter. In particular, S het  may FIG. 4. Band diagram of the optimized GaP/Si PERC cell in an open-circuitcondition. A very high valence-band offset between GaP and Si acts as analmost ideal minority carrier (holes) blocker. Consequently, the hole densityis drastically reduced in the emitter, as shown in Fig. 3, thereby reducing therecombination rate in the GaP layer, as shown in Fig. 2.FIG. 5. Simulated GaP/Si PERC cell efficiency when dependent on the dop-ing density in the Si wafer and in the GaP layer. All other parameters arekept at their optimum values, which are given in Table I.FIG. 6. Simulated GaP/Si PERC cell efficiency when dependent on the GaPelectron affinity  v  and surface recombination velocity in the hetero-interface S het  . All other parameters are kept at their optimum values, which are givenin Table I.FIG. 7. Simulated GaP/Si PERC cell efficiency when dependent on the frontand rear surface recombination velocities and the recombination velocity atthe hetero-interface. All other parameters are kept at their optimum values,which are given in Table I. 044508-5 Wagner  et al.  J. Appl. Phys.  115 , 044508 (2014)
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